Consensus is how thousands of independent computers agree on one shared truth: which transactions happened and who owns what. In Bitcoin it happens without a leader, a vote or a central server.
Two layers of agreement
1. Agreeing on the rules. Every node runs software that enforces the same rules: no more than 21 million coins, valid digital signatures, no double spending, correct block reward, and so on. These are the "consensus rules". A block that breaks any of them is rejected by every honest node, no matter how much work went into it.
2. Agreeing on history. Among all valid chains, nodes follow the one with the most accumulated proof of work. If two miners find blocks at once, the chain briefly forks. The next block usually settles it, and everyone moves to the heavier branch.
Nakamoto consensus
This combination, rules checked by everyone plus the "most work wins" principle, is often called Nakamoto consensus. Its strength is that it is open: anyone can join as a node or a miner without permission.
Changing the rules
Because every node enforces the rules, changing them requires broad agreement. A soft fork tightens the rules in a backwards-compatible way. SegWit (2017) and Taproot (2021) were soft forks. A hard fork loosens or changes rules so that old nodes would reject the new blocks. The 2017 split that created Bitcoin Cash was a hard fork.
Why it matters
Consensus is what makes Bitcoin's rules hard to change. Not developers, not miners and not exchanges can force a change on users who run their own full nodes. Each node decides for itself, and together they keep the network honest.